Least Common Multiple

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Find the *Least Common Multiple* (LCM) of the numbers 1400 and 1350.

**Answer**

$1400=({2}^{3})({5}^{2})(7)$

$1350=(2)({3}^{3})({5}^{2})$

The LCM of 1400 and 1350 is the product of the largest powers of each prime factor in both.

Thus the LCM of 1400 and 1350

$=({2}^{3})({3}^{3})({5}^{2})(7)$

$=37800$